When we want to divide a line drawn through two points P and Q with a ratio m:n, the coordinates of the point M can be given as
[tex]M=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})_{}[/tex]
If
[tex]\begin{gathered} Q\to(x_1,y_1)=(-2,2) \\ P\to(x_2,y_2)=(2,5) \end{gathered}[/tex]
The ratio m:n will be 1:4, given that M is located at one-fifth of the distance from Q to P.
Hence, the coordinates are
[tex]M=(\frac{\lbrack1\times2\rbrack+\lbrack4\times-2\rbrack}{4+1},\frac{\lbrack1\times5\rbrack+\lbrack4\times2\rbrack}{4+1})[/tex]
Solving, we have
[tex]\begin{gathered} M=(\frac{2-8}{5},\frac{5+8}{5}) \\ M=(-1.2,2.6) \end{gathered}[/tex]
The correct option is the THIRD OPTION.
